which number line represents the solution set for the inequality 3x < -9?

Answer:

The third number - line (the one with an open - circle at $x=-3$ and the arrow pointing to the left).

Explanation:

Step1: Solve the inequality

Divide both sides of $3x < - 9$ by 3. $x<\frac{-9}{3}$

Step2: Simplify the right - hand side

$x < - 3$ Since $x$ is strictly less than $-3$ (not equal to $-3$), we use an open - circle at $x = - 3$ on the number line, and the values of $x$ that satisfy the inequality are to the left of $-3$, so the arrow points to the left.